Arbeitspapier

Propriety of posteriors in structured additive regression models: theory and empirical evidence

Structured additive regression comprises many semiparametric regression models such as generalized additive (mixed) models, geoadditive models, and hazard regression models within a unified framework. In a Bayesian formulation, nonparametric functions, spatial effects and further model components are specified in terms of multivariate Gaussian priors for high-dimensional vectors of regression coefficients. For several model terms, such as penalised splines or Markov random fields, these Gaussian prior distributions involve rank-deficient precision matrices, yielding partially improper priors. Moreover, hyperpriors for the variances (corresponding to inverse smoothing parameters) may also be specified as improper, e.g. corresponding to Jeffery's prior or a flat prior for the standard deviation. Hence, propriety of the joint posterior is a crucial issue for full Bayesian inference in particular if based on Markov chain Monte Carlo simulations. We establish theoretical results providing sufficient (and sometimes necessary) conditions for propriety and provide empirical evidence through several accompanying simulation studies.

Sprache
Englisch

Erschienen in
Series: Discussion Paper ; No. 510

Thema
Bayesian semiparametric regression
Markov random fields : MSMC
penalised splines
propriety of posteriors

Ereignis
Geistige Schöpfung
(wer)
Fahrmeir, Ludwig
Kneib, Thomas
Ereignis
Veröffentlichung
(wer)
Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
(wo)
München
(wann)
2006

DOI
doi:10.5282/ubm/epub.1879
Handle
URN
urn:nbn:de:bvb:19-epub-1879-0
Letzte Aktualisierung
10.03.2025, 11:45 MEZ

Datenpartner

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ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.

Objekttyp

  • Arbeitspapier

Beteiligte

  • Fahrmeir, Ludwig
  • Kneib, Thomas
  • Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen

Entstanden

  • 2006

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